This is my reading; I’m not consulting some expert’s interpretation.
I think he’s saying that all death is one; that from the beginnings of humanity, mortality is part of the package, and it doesn’t set anyone apart; rather, it unites us.
So, he says, he’s not going to “murder / The mankind of her going”—not going to detract from her absorption into the common lot of humanity—by treating it as something unusual. An “elegy of innocence and youth” would “blaspheme down the stations of the breath.”
The child lies “deep with the first dead”—the first dead, the elders of our race. Death has been with us from the beginning, and it won’t end until the world ends (“the last light breaking”). Not only death but the mourning of death is a human thing, not part of unconscious nature (“by the unmourning water / Of the riding Thames”), and every death is all that one same death.